The lattice symmetry and grain orientations in microstructures
are known to affect physical properties of materials. For example,
lithium diffusion in a battery electrode induces lattice deformation
[1]}, [2]}, [3]}, [4]},
which affects lithium ion kinetics [1]} and causes anisotropic
expansion of electrodes [2]}.
Likewise, in a paraelectric to ferroelectric phase transitions, lattices
transform from centrosymmetric to other point groups lacking an inversion
centre. This transformation introduces stress-free spontaneous strains
in the ferroelectric system [7]}. At present, theoretical
models like phase field methods describe complex microstructures in
electrode/ferroelectric systems as a function of the composition field
(lithium-ion concentration, temperature or polarization) [8]}, [9]}, [10]}, [11]}.
The Kobayashi-Warren-Carter phase field model [4]}
further accounts for crystallographic misorientation at grain boundaries
during a phase transition process. While these modeling approaches
provide insights on the position of phase and grain boundaries, they
only account for grain orientations as an empirical parameter [4]}.
The current phase field approaches do not allow for lattices to distort
independently. Consequently, the local strain fields arising from
individual lattice distortions and the presence of defects in a material
system are not explored.
